NASA/TM--2000-209594

Analytic Guided-Search Model of Human

Performance Accuracy in Target-Localization

Search Tasks

Miguel P. Eckstein, Brent R. Beutter, and Leland S. Stone

Ames Research Center, Moffett Field, California

April 2000

https://ntrs.nasa.gov/search.jsp?R=20010038016 2018-05-15T06:51:32+00:00Z
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NASA/TMm2000-209594

Analytic Guided-Search Model of Human

Performance Accuracy in Target-Localization

Search Tasks

Miguel P. Eckstein

Cedars Sinai Medical Center

UCLA School of Medicine, Los Angeles, California

Brent R. Beutter

San Jose State University Foundation

San Jose State University, San Jose, California

Leland S. Stone

Ames Research Center, Moffett Field, California

National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, California 94035

April 2000
Acknowledgments

The authors would like to thank Drs. AI Ahumada and Roger Remington for useful comments on earlier

drafts. This work was supported by NASA 50827 and NCC 2-1027 to MPE, and NASA RTOPs 711-51-12

and 131-20-30 to LSS.

NASA Center for AeroSpace Information

7121 Standard Drive

Hanover, MD 21076-1320

301-621-0390

Available from:

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

703-605-6000

This report is also available in electronic form at http://www.csmc.edu/medphys/vp.html
Summary

Current models of human visual search have

extended the traditional serial/parallel

search dichotomy. Two successful models

for predicting human visual search are the

Guided Search model and the Signal

Detection Theory model. Although these

models are inherently different, it has been

difficult to compare them because the

Guided Search model is designed to predict

response time, while Signal Detection

Theory models are designed to predict

performance accuracy. Moreover, current

implementations of the Guided Search

model require the use of Monte-Carlo

simulations, a method that makes fitting the

model' s performance quantitatively to

human data more computationally time

consuming. We have extended the Guided

Search model to predict human accuracy in

target-localization search tasks. We have

also developed analytic expressions that

simplify simulation of the model to the

evaluation of a small set of equations using

only three free parameters. This new

implementation and extension of the Guided

Search model will enable direct quantitative

comparisons with human performance in

target-localization search experiments and

with the predictions of Signal Detection

Theory and other search accuracy models.

Introduction

In standard visual-search tasks, the observer

looks for a target among a set of distractors.

When the target differs greatly from the

distractors along a single feature dimension

(e.g. contrast, orientation, color, etc.), the

time to find the target is relatively constant

as a function of the number of elements (set

size). This fact is commonly interpreted as

evidence for parallel search (i.e. the

simultaneous examination of potential

targets). Alternatively, when the target is

similar to the distractors, the distractors are

heterogeneous, or the target can be

differentiated from the distractors only by

the combination of two or more feature

dimensions (conjunctions), the response

time increases drastically with set size. This

finding is commonly interpreted as evidence

for a temporally serial search (i.e. the

sequential examination of potential targets).

Although the parallel/serial dichotomy has

dominated research for more than two

decades (refs. 1-4), and is central to many

theories of visual search (e.g., Feature

Integration Theory; ref. 5), more recently,

models of visual search have moved away

from the original strict serial/parallel

dichotomy.

There have been two traditions in studying

the processes mediating visual search. One

approach has been to allow extended

viewing of the stimulus and to measure

observer response times (e.g., refs. 6-8),

while a second approach has been to use

fixed duration displays and to measure

detection accuracy, the probability of

correctly detecting the presence of the target

(e.g., refs. 9, 10). The response-time results

can be predicted by a two-stage Guided

Search (GS) model (refs. 6, 11) in which an

initial parallel system guides a subsequent

serial-search stage. The accuracy results

can be predicted by a single-stage Signal

Detection Theory (SDT) model (ref. 12) in

which processing is parallel but noisy (e.g.

refs. 9, 10, and 13-16). Even though the GS

and SDT models are based on

fundamentally different assumptions about

human visual information processing,

progress in our understanding of search has

been hampered by the difficulty associated

with directly comparing these two models

because they were developed for different

experimental paradigms and are applicable

to different empirical measurements. A

second difficulty is that current

implementations of the GS model (ref. 11)

require Monte-Carlo simulations, which

make fitting the model to human data more

computationally time consuming.

This report describes an analytic extension

of the GS model, the Guided Search

Accuracy (GSA) model, which predicts

performance accuracy in a target-
localizationsearchtaskasafunctionof set

size. We develop analytic mathematical

expressions that allow quantitative fitting of

the model to human data in a time-efficient

manner using only three free parameters.

The significance of this implementation and

extension is that it will allow the direct and

quantitative comparison of Guided Search

and Signal Detection Theory models in

target-localization search tasks.

Theory

The Guided Search model

The GS model (ref. 11) was developed to

predict response times as a function of set

size in one type of visual search task. In

this type of search experiment, there are two

kinds of displays: target-present and targetabsent. Each consists of N elements. In

target-present trials, one element, the target,

differs from the others, the distractors, while

in target-absent trials, all the elements are

distractors. The observer's task is to search

the display to determine whether it is a

target-present trial or target-absent trial and,

as quickly as possible, to make a response

indicating the decision. The dependence of

the response times on the set size is

measured.

The GS model assumes that each element is

processed by broadly tuned channels that

correspond to categorical features (e.g.

"red'.', "green", "bright", etc.). The bottomup response of each element is determined

by a weighted average of the difference in

output between that element and its

neighbors. The top-down response is a

function of the match of the element to the

designated target. The final internal

response associated with a given element is

a weighted sum of the top-down and

bottom-up responses. This final response is

perturbed by the addition of internal neural

noise, assumed to be Gaussian, to yield a

final "activation" for each element. Finally,

visual attention serially searches through

those elements, whose activations are above

2

a threshold (L), according to a selfterminating procedure. Unlike the standard

serial search model where visual attention

proceeds randomly from one element to

another (ref. 5), in the GS model, visual

attention proceeds in an activity dependent

order. It begins with the element that

elicited the highest activation and continues

in order of decreasing activation. The search

terminates when either the target is found,

or no elements remain with activation above

the activation threshold. Rejected elements

are not revisited. It is assumed that

attending to each element requires a fixed

amount of processing time, and thus that the

response time is determined by the total

number of elements searched, and also that

if the target is attended, the observer always

correctly identifies that trial as a targetpresent trial. If the search is terminated

without processing the target (because the

target did not exceed threshold), the

observer guesses "target absent" 97 % of the

time and "target present" 3 % of the time.

The Guided Search Accuracy model

We have developed an analytic extension of

the GS model, the GSA model (Fig. 1),

which predicts accuracy in a localization

search task. In localization search tasks, a

fixed-duration display containing a single

target and a number of distractors is

presented to the observer. The observer

then reports which of the N locations

contains the target. The accuracy of

correctly identifying the target location is

measured as a function of set size (N). The

structure of the GSA model is nearly

identical to the GS model, except that to

predict localization accuracy for fixed

stimulus durations, the serial attention stage

of the GSA model is restricted to examining

a fixed number of elements. If the target

has not been found within the restricted

presentation time, the model is forced to

guess.

The GSA model consists of two stages: a

noisy parallel-processing stage and a noise-
freeserial-attentionstage.In theparallelprocessingstage,eachelementinthe

displayelicitsanoisyresponse, its

activation.Weassumethateachelement's

activationcanbedescribedbyaGaussian

probabilitydistribution,andthatthetarget

anddistractordistributionshaveequal

variances'.A targetelicits,onaverage,a

largeractivationthanadistractor(Fig.2).

Thetarget-distractor discriminabilityisd', a

measureof thedistancebetweenthetarget

anddistractordistributions.Theresultsof

thisparallelprocessingstagearethensent

tothenoise-freeserialattentionstage,that

firstordersthesupra-thresholdelements

(thosewithactivationsgreaterthanthe

threshold,_,)accordingtotheiractivation.

Then,visualattentionseriallyprocessesthe

supra-thresholdelements,beginningwith

theelementwiththehighestactivationand

continuingindecreasingorderof activation

(Fig.1).Processingeachelementwith

visualattentionrequiresafixedamountof

timeandprocessingcontinuesuntilall

supra-thresholdelementshavebeen

processedorthetargetisfound,oruntil the

displaypresentationends.If visual

attentionprocessesthetarget,themodel

alwayscorrectlyidentifiesthelocationof

thetarget(evenif itsactivationfromthe

initialparallelprocessingstagewasby

chancelowerthanthatof adistractor)_If

thetargetwasnotprocessedduringthe

displaypresentation, theGSAmodelis

forcedto guess.If all supra-threshold

elementshavenotbeenprocessed, the

modelchoosestheremainingsuprathresholdelementwiththehighest

activation.Otherwise(if all supra-threshold

elementshavebeenprocessed), it chooses

The equal-variance assumption is included to reduce

the number of free parameters in the GSA model, but

can be relaxed by adding a parameter specifying the

ratio of the variance of the target distribution to that of

the distractor.

21n the both the GS and GSA models and in other

models with a serial attention mechanism, visual

attention is assumed to be a homunculus that can

determine without error the identity of an attended

element.

randomly among all remaining subthreshold elements. Errors can occur when

there are either more supra-threshold

elements than can be processed serially

prior to the display being terminated, or

when the activation of the target is subthreshold.

Simplification of the GSA model

To facilitate fitting the analytic GSA model

to human performance data, we have

simplified the original model (ref. 11) by

reducing the number of free parameters.

First, because in most target-localization

search tasks, the observer is searching for an

a priori known target and not an odd-man

out, we assume that the responses of the

parallel processing stage are entirely

determined by the similarity of an element

to the known target (top-down activation).

Thus, we assume that the contribution of the

bottom-up processing is negligible; either

the output associated with an element does

not depend on a weighted average of the

difference of filter outputs for that element

and its neighbors (no lateral inhibition), or if

it does, this effect does not vary across setsize conditions (constant lateral inhibition)?

Therefore the GSA model is applicable to

search displays that contain widely spaced

elements or that maintain a constant interelement distance for all set sizes. Second,

we assume that the activation threshold and

the maximum number of elements serially

processed are constant across trials. All

other aspects of the model are identical to

those of the Guided Search model 2.0 (ref.

11).

3The GSA model could be extended to include effects

of lateral inhibition if an appropriate model of how

target detectability varies as a function of element

density is specified. Alternatively, lateral interactions

between the activity elicited by each element can be

avoided if the elements are far apart such that the

distance between elements is large relative to their

size.

3
Analytic implementation of the GSA

model

We have developed analytic expressions for

the performance accuracy (% correct) of the

GSA model. Because both the target and

distractor distributions are equal variance

Gaussians, without loss of generality, we

can rescale these distributions so that: 1)

both target and distractor distributions have

unit variance, 2) the mean distractor

activation is zero, 3) the mean target

activation is d'. Thus, the probability of a

distractor producing an activation x is:

1

d(x) = _exp(-x 2 / 2) (1)

The probability of the target producing an

activation x is:

1 _d,) 2

t(x)=--_exp(-(x /2)

(2)

We denote the cumulative probability of a

distractor producing an activation less than

x by

x

19(<x)= J d(x)dx, (3)

the probability of a distractor producing an

activation greater than x by

El(> x) = id(x)dx, (4)

the probability of the target producing an

activation less than x by

4

x

T(< x)= It(x)dx, (5)

and the probability of the target producing

an activation greater than x by

T(> x) =it(x)dx.

x

(6)

We compute the probability of the GSA

model correctly locating the target in two

separate regimes: 1) when the target

activation is supra-threshold'(i.e, larger than

K), 2) when the target activation is subthreshold. Because, in many experiments,

the display duration is fixed (usually brief:

50-300 ms) and examining each element

requires a fixed amount of processing time,

there is time to serially examine at most k

elements, which may be less than the total

number of supra-threshold elements. Thus,

we assume that on each trial, at most k

elements are serially examined, and that k is

less than or equal to N (if k>= N, there is

time to search all the elements). If the

target is examined, the model always

correctly chooses it2. Otherwise, the model

chooses the element with the next highest

activation threshold, or if none of the

remaining elements is supra-threshold, it

randomly guesses among the sub-threshold

elements.

In the first regime, when the target

activation is supra-threshold, there are two

ways the model can correctly identify the

target: 1) if the target ranks among the k

highest activations, it is guaranteed to be

processed and thus is always correctly

located, 2) if the target has the k+l highest

activation, it is next in line at the end of the

trial, so the model correctly chooses it'

' Instead of choosing the k+l _ element, a variation of

the model could guess among all unprocessed

elements. This latter version of the model produces

slightly worse performance for a given set of
Otherwise, it incorrectly chooses the

distractor, which is next in line. Thus, for

supra-threshold targets, the target is always

correctly chosen if it is among the k+l

highest activation, and is never correctly

chosen if it is not. To explicitly compute

the probabilities, it is necessary to consider

all possible permutations of distractor

labeling, which is performed in the factorial

terms of the subsequent equations.

The probability of a correct response given

that the target is supra-threshold and is

among the k+l highest activations (Pc,) is

the sum from j -- 1 to k+ I of the probability

of the target being supra-threshold and

being the j_ highest activation. Each term is

the product of the probability of the target

taking a value x, the probability of exactly j1 distractors taking a value larger than x, the

probability of exactly N-j distractors taking

a value less than x, times a binomial

coefficient describing the number of

possible distractor permutations:

(7)

k+l _V I" +*" 2(7,)I, x>EO<> x J'

j=l 2

Therefore, percent correct localization for

the case in which the target activation is

supra-threshold can be calculated as the sum

of the probabilities of the target activation

ranking among the k+l highest activations

(Pc,).

In the second regime, the target activation is

sub-threshold, and is sometimes correctly

guessed from all the unprocessed elements

(Pc2). If the number of supra-threshold

distractors, j, is greater than k, the model

processes k distractors and then chooses the

distractor next in line, and so is never

correct. If the number of supra-threshold

distractors, j, is less than or equal to k, the

parameters than the version presented here. However,

the two models have virtually identical sensitivity to

variations in the parameters.

model first processes all j supra-threshold

distractors and then randomly chooses one

of the N-j sub-threshold elements.

Therefore, it is correct only if this random

choice is the target, which occurs with a

probability of I/(N-j). The probability of a

correct guess (Pc2) is then the sum over j

equal 0 to k of I/(N-j) times the product of

the probability of the target being subthreshold, the probability of exactly j

distractors being supra-threshold, and a

binomial coefficient describing all possible

distractor permutations:

(8)

Pc2 = _ . T(< ,;t)[D(> A)lJ[D(< 2)1 t_-'-j> \) /_N-))

j=O

Because the two possibilities described by

Eq. 7 and 8 are mutually exclusive, the total

percent correct in the localization of the

target for the GSA model is the sum of these

two independent probabilities:

Pc = Pc, + Pc 2 (9)

Results

We investigated the model's performance

(Pc) as a function of its three free

parameters: the activation threshold (X), the

maximum number of elements that can be

processed serially within the presentation

time (k), and the discriminability between

the target and distractors (d').

Effect of the activation threshold

The activation threshold is a primary cause

of performance errors for the GSA model.

Figure 3 shows the probability distributions

of the number of supra-threshold distractors

for a display with 6 distractors (N=7) for

four different values of the activation

threshold ([mel]X = -10, 0, 1, 2). The

probabilities of the target (d'=l) exceeding

the threshold are 0.98, 0.84, 0.5 and 0.17,

respectively, for these activation thresholds.

When there is no activation threshold (or it

is very negative) then the activations of all 6

distractors are always supra-threshold. As

5
the threshold is increased, the expected

number of distractors exceeding threshold

decreases and for high thresholds the shape

of the distribution also changes (Fig. 3).

Similar decreases in the probability of the

target's activation exceeding threshold also

occur. Thus, an increase in the activation

will generally decrease performance

accuracy for two reasons. First, it decreases

the probability that the target is suprathreshold and thus that it is examined by the

serial processor, which forces the model to

guess more frequently. Second, it decreases

the number of distractors that are examined

by the serial processor and discarded from

the guessing subset.

For those set-size conditions in which the

number of elements in the display is small

so that all (or all but one) of the elements

can be processed serially (N < k + 1), the

activation threshold is the only source of

performance errors. If there were no

activation threshold, for N<k the model

would serially process every element in the

display and would always correctly identify

the target (Pc =100). Similarly if N--k+l,

the model would serially examine N-1

elements, then correctly guess the remaining

element (if it hadn't already found the

target) again producing perfect

performance. Figure 4 shows the decrease

in performance caused by increasing the

activation threshold for a fixed k = 4 and d'

= 1.0. As the activation threshold is

increased, there is an increasing probability

that the target activation is sub-threshold,

and that the model incorrectly chooses a

distractor. If the target is sub-threshold, the

model first examines the supra-threshold

distractors. If the number of suprathreshold distractors is greater than k, then

the model incorrectly chooses the k+l _

distractor. If the number of number of

supra-threshold distractors is less than k,

then the model is forced to guess randomly

among the remaining elements. For high

thresholds, the guessing is less accurate

because there are a larger number of sub6

threshold distractors. Therefore, a high

threshold lowers performance, because it

causes the model to guess more frequently

and less accurately.

Effect of the maximum number of

elements serially processed (k)

The time limit imposed on the serial

allocation of visual attention is the second

source of errors for the GSA model. If an

element is processed in x ms and the

processing is temporally serial, then in a

presentation time "_,the model can only

process k = x/x elements. Therefore, if

there are N > k+l elements, the model will

be unable to process all of the elements

necessary to make a perfect decision. There

will be a non-zero probability that the target

is not processed by serial attention. In these

cases the model incorrectly chooses the

k+l _ element. Alternately, when there are

N < k+l elements, the serial processor will

be able to process all N-I elements

necessary for a perfect decision unless the

target itself is sub-threshold (i.e. no errors

will be generated due to the serial

processing time). Figure 5 shows the

performance accuracy as a function of set

size for four different values of the

maximum number of serially processed

elements (k = 2, 4, 6, and 8). Increasing k

changes the set size at which performance

degrades due to the serial processing

(inflection point in the curve) and the rate at

which performance degrades (downward

trend of the curve). Figure 5A shows that

changes in k can greatly affect performance

for a low activation threshold (_, = 0).

Figure 5B shows the effect of varying k is

much less dramatic for a larger activation

threshold (_, -- 1). Thus, when _, is high,

most errors are generated by _, itself, and

changes in k do not affect performance as

much. This is because _, (together with N)

determines the average number of suprathreshold elements. A high _, limits the

effective number of elements available to

the serial processor. If the effective (as

opposed to actual) number of elements is
large,thenperformanceislimitedlargely by

k. If it is smaller than k, then performance

is mostly limited by k.

Effect of target-distractor

discriminability (d')

In the GSA model, target-distractor

discriminability is determined by the

distance between the target and distractor

distributions (Fig. 2). Decreasing the

physical difference between the target and

the distractors decreases the difference

between the mean activation of the target

(d') and the mean activation of the

distractor (always zero). As the targetdistractor discriminability is reduced, the

probability that the target does not rank

among the k highest activations increases,

thereby increasing errors. In addition, the

probability that the target activation does

not exceed threshold also increases thereby

generating even more errors. As a result,

decreasing target-distractor discriminability

will reduce the GSA model performance.

Figure 6 shows the model's performance

accuracy for four levels of target-distractor

discriminability (d' = 2.0, 1.5, 1.0, 0.5) as a

function of set size for k=4. Figure 6A

shows accuracy for _. = 0 and Figure 6B for

_, = 2. These results show that d' is an

important factor that influences

performance in two ways. First, d'

determines the overall level of performance,

lower d' values produce less accurate

performance for all conditions examined

(downward shift). Second, lower d' values

increase the observed set-size effects. In

particular, for high thresholds (_, = 2), as

shown in Figure 6B, performance initially

decreases rapidly as a function of set size,

then decreases much more slowly. The set

size for which this change is observed

depends on the value of d'; high d' values

produce a rapid decrease in performance

only for small set sizes, while low d' values

produce rapid decreases in performance

over a larger range of set sizes.

Monte Carlo Simulations

To verify that the analytic expressions

above (Eqs. 1-9) accurately describe the

GSA model, we compared the results from

these expressions with predictions from

standard Monte Carlo simulations of the

sequence of probabilistic events described

in Fig. 1. Performance predictions for the

GSA analytic expressions were in good

agreement with results from the brute force

Monte-Carlo simulations of the model

across the range of parameter settings

tested.

Conclusions

We have developed an extension of the

Guided Search model, the GSA model,

which uses explicit analytic expressions to

compute accuracy in a target-localization

task. Our implementation allows the

performance accuracy of the Guided Search

model to be directly compared to that of

human observers, the SDT model, or any

other model of target-localization accuracy.

We explicitly investigated the effect of

varying three model parameters (activation

threshold, maximum number of elements

serially processed within the presentation

time, and the target-distractor

discriminability) on localization accuracy as

a function set size. The GSA model will

facilitate the direct and quantitative

comparison of the ability of the Guided

Search and Signal Detection Theory models

to explain human search performance in

target-localization tasks.

7
References

. Kinchla, R.A.,(1974) Detecting targets

in multi-element arrays: A confusability

model. Perception & Psychophysics, 15,

149-158

. Schneider, W.,and Schiffrin, R.M.,

(1977). Controlled and automatic

human information processing: I.

Detection, search and attention.

Psychological Review, 84, 1-66.

. Bergen, J. R. and Julesz, B. (1983a).

Rapid discrimination of visual patterns.

IEEE Transactions on Systems, Man,

and Cybernetics, 13, 857-863.

° Bergen, J. R. and Julesz, B. (1983b).

Parallel versus serial processing in rapid

pattern discrimination, Nature, 303,

696-698.

. Treisman, A. M. and Gelade, G. (1980).

A feature integration theory of attention.

Cognitive Psychology, 12, 97-136.

6. Wolfe J. M., Cave, K. R., Franzel S.L.

(1989). Guided search: an alternative to

the feature integration model for visual

search. Journal of Experimental

Psychology: Human Perception &

Performance, 15, 419-433.

. Treisman, A. M.(1991). Search,

similarity, and integration of features

between and within dimensions, Journal

of Experimental Psychology: Human

Perception & Performance, 17(3), 652-

676.

. Duncan J., Humphreys G.W. (1989),

Visual search and stimulus similarity.

Psychological Review, 96, 433-458

. Palmer, J. (1994). Set-size effects in

visual search: the effect of attention is

independent of the stimulus for simple

tasks. Vision Research, 34, 1703-1721.

10.

11.

12.

13.

14.

15.

16.

Eckstein, M.P. (1998). The lower

efficiency for conjunctions is due to

noise and not serial attentional

processing, Psychological Science, 2,

111-118.

Wolfe, J.M. (1994). Guided search 2.0:

A revised model of visual search.

Psychonomic Bulletin & Review, 1,

202-238.

Green, D. M. and Swets, J. A. (1966).

Signal detection theory and

psychophysics. New York: Krieger

Shaw, M.L. (1980) Identifying

attentional and decision making

components in information processing.

In R. S. Nickerson (Ed.), Attention &

performance VIII (pp. 227-296).

Hillsdale, NJ:Erlbaum.

Palmer, J., Ames, C. T. and Lindsey, D.

T. (1993). Measuring the effect of

attention on simple visual search.

Journal of Experimental Psychology:

Human Perception and Performance,

19, 108-130.

Eckstein, M.P., Beutter. B.R., Stone,

L.S. (1998). The effect of set-size on the

relation between saccadic and

perceptual decisions during search,

Invest. Ophth. & Vis. Sci.(Suppl.), 39,

1031.

Eckstein, M.P., Whiting, J.S. (1996).

Visual signal detection in structured

backgrounds I: The effect of number of

spatial locations and signal contrast.

Journal of the Optical Society of

America A, 9, 1777-1787.

8
Noise

Parallel

Process

(thresholding)

Serial

Process

(attention)

Pick at random a subthreshold element

,Pickrem nin e,oment I with highest activation Yes

Farget?U] M R4__No i N__O I -_ Guess slP_ethrest_?l d

Yes Yes

No

_ Any remaining

timed out

Yes or

/_ __ r____runout of elements

Correct Response J

Figure 1. Schematic of the Guided Search Accuracy model. The parallel processing stage

generates a noisy response for each element (its activation). If this activation is above a

threshold (_.), it is passed to the serial processing stage. Attention sequentially examines

the k highest activations (only those that are suprathreshold) in descending order and

always correctly identifies the target if was examined. If it runs out of time or suprathreshold elements, it guesses. If it runs out of time before running out of suprathreshold

elements, it picks the unexamined element with the highest activation. If it runs out of

supra-threshold elements, it randomly picks one of the subthreshold elements.

9
0.5

0.4

"--- 0.3

_0.2

n

0.1

0

-6 6

Activation

• thdi:_rhaCl tdo(r_ target

,i

|

-4 -2 d 2 4

Intemal Response

Figure 2. Probability distributions of the responses for the target and a distractor. The

response distribution of a target whose d' is 1 is illustrated.

m

e_

o

el

0:}

0.6 ii

0.4 I:,_

0.2

o&,-_ e _.-._. :-, _, , .

0 2 4 6 8 10 12

Number of items above threshold

-"_"-- X=-I 0

- "El-- "L=O

--&" ' L=I

-'o- L=2

14

Figure 3. Probability distributions of the expected number of supra-threshold elements for

different values of activation threshold for a fixed target-distractor discriminability (d' =

1.0) and set size (N= 7).

10
100

80

8o

8

._ 40

o=

20

0 2 4 6 8 10 12 14

Set-size

___ -10

0

- 1.0

[ok= 2.0

Figure 4. Accuracy (Pc) as a function of set size for different values of activation

threshold (_,) for a fixed maximum number of serially processed elements (k = 4), and a

fixed target-distractor discriminability (d" = 1.0).

11
A

100

80

ooo

40

O

L..

q)

a.. 20

0

0

i i I I 1 I

2 4 6 8 10 12 14

Set-size

ok=2

[] k=4

A k=6

ok=8

B

100

80

60

tO

• 40

0

L.

a. 20

0

k=l_

i i i i 1

0 2 4 6 8 10 12 14

Set-size

Figure 5. Accuracy (Pc) as a function of set size for different values of the maximum

number of serially processed elements (k = 2, 4, 6, and 8), for two different activation

thresholds, and a fixed target-distractor discriminability (d' = 1.0). A) E= 0, B) _. = 1.

12
100

80

8 6o

_ 40

a. 20

I _ I 1 I 1

0 2 4 6 8 10 12 14

Set-size

od'=2.0

Dd'= 1.5

Ad'= 1.0

od' =0.5

100

80

8 60

40

a. 20

I I I I I I

0 2 4 6 8 10 12

Set-size

14

od' =2.0

Dd'= 1.5

z_d'= 1.0

od' =0.5

Figure 6. Accuracy (Pc) as a function of set size for different values of target-distractor

discriminability (d' = 0.5, 1.0, 1.5 and 2.0), for two values of activation threshold and a

fixed maximum number of serially processed elements (k = 4). A) _,= 0, B) _, = 2.

13
Form Approved

Report Documentation Page OMB No. 0704-0188

_ reponiagb_KIm_ this¢elsctmo_iaton_eJon isestimmdtoavaage1ho_perreq)onse, includ_gh _ _ _ _, _ a_ _ _ _ n _ _ _

teeded,m¢l¢OmlPle(i_md _ the¢o_ ol ir_. SerKIcommen_ n_a_g this b_ e_e ot arc/olMr _ d _ _ _ _, _ _ _ _ _ _, _

W_ Hmdq_em S_. Oncto_ forlnlo_ Op_ imdRq_, 1215 Je_mDonDevil Hi_q_, Soite 1204, J_ington,VA 22202-4302, _ _ _ _ _ _ _ _, P_

Project(0704.0188), Wmhinglon,OC205_.

1.AGENCYUSEONLY(Leaveblank) 2. REPORTDATE 3. REPORTTYPEANDDATESCOVERED

April 2000

4. TITLEANDSUBTITLE

Analytic Guided-Search Model of Human Performance Accuracy in

Target-Localization Search Tasks

6.AUTHOR(S)

Miguel P. Eckstein, Brent R. Beutter, and Leland S. Stone

7.PERFORMINGORGANIZATION NAME(S) ANDADDRESS(ES)

NASA Ames Research Center

Moffett Field, California 94035-1000

9.SPONSORING/MONITORING AGENCYNAME(S) ANDADDRESS(ES)

National Aeronautics and Space Administration

Technical Memorandum

5. FUNDINGNUMBERS

711-51-12

8. PERFORMINGORGANIATION

REPORTNUMBER

IH-011

10.SPONSORING/MONITORING

AGENCYREPORTNUMBER

NASA/TM--2000-209594

11.SUPPLEMENTARYNOTES

Point of Contact: Leland S. Stone, Ames Research Center, M/S 262-2, Moffett Field, CA 94035

(650) 604-3240

12A. DISTRIBUTION/AVAILABIUTYSTATEMENT 12B.DISTRIBUTIONCODE

Subject Category: 53-01 Distribution: Public

Availability: NASA CASI (301) 621-0390

13. ABSTRACT(Max/mum200 words)

Current models of human visual search have extended the traditional serial/parallel search

dichotomy. Two successful models for predicting human visual search are the Guided Search

model and the Signal Detection Theory model. Although these models are inherently different, it

has been difficult to compare them because the Guided Search model is designed to predict

response time, while Signal Detection Theory models are designed to predict performance

accuracy. Moreover, current implementations of the Guided Search model require the use of

Monte-Carlo simulations, a method that makes fitting the model's performance quantitatively to

human data more computationally time consuming. We have extended the Guided Search model

to predict human accuracy in target-localization search tasks. We have also developed analytic

expressions that simplify simulation of the model to the evaluation of a small set of equations

using only three free parameters. This new implementation and extension of the Guided Search

model will enable direct quantitative comparisons with human performance in target-localization

search experiments and with the predictions of Signal Detection Theory and other search

accuracy models.

14.SUBJECTTERMS

Search, Human performance, Visual detection

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19. SECURITY CLASSIFICATION

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Unclassified

15. NUMBER OF PAGES

18

16. PRICECODE A03

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